Generalized derivations acting on multilinear polynomials in prime rings
Let be a prime ring with its Utumi ring of quotients and extended centroid . Suppose that is a generalized derivation of and is a noncentral Lie ideal of such that for all , where is a fixed integer. Then one of the following holds:
Let be a prime ring and a nonzero ideal of The purpose of this paper is to classify generalized derivations of satisfying some algebraic identities with power values on More precisely, we consider two generalized derivations and of satisfying one of the following identities:
Let be a prime ring with center and a nonzero right ideal of . Suppose that admits a generalized reverse derivation such that . In the present paper, we shall prove that if one of the following conditions holds: (i) , (ii) , (iii) , (iv) , (v) , (vi) for all , then is commutative.